WASHINGTON — Fresh from a successful battle against a Democratic opponent, Donald Trump's attention must now turn to defining his presidency.

His campaign offered two divergent approaches. He was a disruptive bomb-thrower when it came to general demeanor and his immigration and national security stances. He was a more conventional Republican when it came to his social-issue positions and economic concerns.

The warring options were on sharp display overnight into Friday.

Responding to protests around the country Thursday night, Trump first issued a tweet in keeping with the defiant tone of his campaign that “professional protesters, incited by the media, are protesting. Very unfair!”

Nine hours later came one that was more presidential in approach, if a reversal from his first sentiment.

“Love the fact that the small groups of protesters last night have passion for our great country. We will all come together and be proud!” he said.

The early discussions about key positions in his administration included similarly opposed sentiments, suggesting that Trump has yet to lock down how he will approach governing the nation.

Among those being considered for presidential chief of staff — the figure who more than any other determines how well a White House works, and at what — was Stephen Bannon, who took a leave as chairman of Breitbart News to serve as Trump's campaign CEO.

Bannon is a controversial figure even among Republicans, seen in the campaign as encouraging Trump's more eye-opening stunts such as his news conference with several women who accused former President Bill Clinton of making sexual advances.

He also fanned some of Trump's incendiary rhetoric about immigrants, Muslims and African-Americans.

But he has no experience in governing or keeping on track an organization as large as the executive branch.

Another person being considered was the far more buttoned-down Republican National Committee Chairman Reince Priebus, an establishment figure who has close ties to House Speaker Paul Ryan and other GOP leaders, having helped to run the party for almost six years.

Bannon and Priebus share an alliance with Trump, but little else.

The pick is seen as essential to Trump's direction since the chief of staff often has the president's ear just before a decision is reached.

The picture is no clearer for other top Cabinet posts, such as secretary of state. Trump is considering Sen. Bob Corker of Tennessee, a consensus builder in the Senate who is well-liked across the aisle.

But he is also looking at former United Nations Ambassador John Bolton, one of the most aggressive neoconservative hawks during the George W. Bush administration and a favorite among the Breitbart set.

Adding further uncertainty, on Friday afternoon Trump shook up his transition team, announcing that Vice President-elect Mike Pence would take over, replacing New Jersey Gov. Chris Christie.

As much as staffing, Trump's presidency also will be defined by the issues he chooses to take up early in his administration.

Already, outside groups and Republicans on Capitol Hill, who have control of both houses, are pressuring Trump to make good on myriad — and sometimes competing — campaign promises.

And they are moving into the vacuum formed by the lack of substantive policy proposals in the campaign.

Trump's success in Tuesday's election rested on running against both parties, Democrats and Republicans alike. That suggests that he may end up cutting a distinct path untethered to the traditional lines, even Republican ones.

For now, the president-elect is keeping his options open, at least publicly. In a brief comment to reporters on Capitol Hill on Thursday, he offered only one broad directive.

“We're going to work very strongly on immigration, health care, and we're looking at jobs, big-league jobs,” he said.

In many ways, Trump's positioning is similar to that of Arnold Schwarzenegger when he became governor of California after the 2003 recall.

Like Trump, Schwarzenegger was a hybrid of showman and political leader, running to blow up politics as usual, but without a particularly ideological set of positions.

That helped him win the election, but left him marooned when he ran into trouble trying to put his plans into action.

Trump has similarly made promises that could prove impossible to deliver, whichever path he sets for his administration, said Jon Cowan, president of Third Way, a centrist advocacy group in Washington.

“The distance between the things he said he would do and the actual reality of how he would do them is larger than any nominee for either party I have ever seen,” he said.

Los Angeles Times' Lisa Mascaro and Noah Bierman contributed.

cathleen.decker@latimes.com